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1
Combine mayonnaise, ketchup, relish, horseradish, and Worcestershire sauce in a small bowl. Stir until fully incorporated. The dressing is ready when the colour is a uniform pale coral with no streaks of unmixed ketchup.
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2
Wrap the sliced corned beef loosely in foil and warm it through — in a low oven or briefly in a dry skillet — before assembly. Cold corned beef will not integrate with the melted cheese. It is ready when it yields to the touch and carries visible steam when unwrapped.
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3
Place the sauerkraut in the centre of a clean towel and twist firmly, expelling as much liquid as possible. This is where the sandwich lives or dies: excess moisture will turn the rye bread irreparably soggy during grilling, and no amount of heat will recover it. The drained sauerkraut should feel nearly dry to the hand and hold its shape when pressed.
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4
Lay all four bread slices on a work surface. Spread the Russian dressing on the interior faces of each slice. On two slices, layer Swiss cheese, then warm corned beef, then the drained sauerkraut, then a second layer of Swiss cheese. Close the sandwiches with the remaining bread, dressing-side inward. Butter the exterior faces of both sandwiches.
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5
Place the sandwiches in a buttered skillet over medium heat, or on a flat press. Grill, pressing firmly if using a skillet and a weighted pan, until the bread is golden-brown and crispy on the underside — then turn and repeat. The sandwiches are done when both exterior faces are deep golden-brown and crispy, and the Swiss cheese has melted completely through the stack, visibly binding corned beef and sauerkraut into a unified layer.